Hits:

Indexed by:期刊论文

Date of Publication:2012-06-01

Journal:CZECHOSLOVAK MATHEMATICAL JOURNAL

Included Journals:SCIE、Scopus

Volume:62

Issue:2

Page Number:527-539

ISSN No.:0011-4642

Key Words:cubic mapping graph; cycle; height

Abstract:Let a"currency sign (n) [i] be the ring of Gaussian integers modulo n. We construct for a"currency signn[i] a cubic mapping graph I"(n) whose vertex set is all the elements of a"currency signn[i] and for which there is a directed edge from a a a"currency signn[i] to b a a"currency signn[i] if b = a (3). This article investigates in detail the structure of I"(n). We give suffcient and necessary conditions for the existence of cycles with length t. The number of t-cycles in I"(1)(n) is obtained and we also examine when a vertex lies on a t-cycle of I"(2)(n), where I"(1)(n) is induced by all the units of a"currency signn[i] while I"(2)(n) is induced by all the zero-divisors of a"currency signn[i]. In addition, formulas on the heights of components and vertices in I"(n) are presented.